For me, it's more a collection of memories rather than a tangible set of reasons on why the Amiga was better than the competition.
Playing with an Action Replay on my A500 and learning about the guts of Amiga hardware. The game cheating and mod ripping was also fun. :-)
Getting "baggies" of the latest demos out of Europe complete with a hand-written letter from friends overseas.
Rushing to the newsagent to get the latest Amiga Format magazine complete with a free(!) coverdisk and later A.C.A.R. (Australian Commodore and Amiga Review). I still have 5 or 6 boxes of these things.
Being blown away when I saw the Odyssey demo by Alcatraz, something I still enjoy watching on my XBox.
Being totally blown away when I saw Spaceballs/State Of The Art.
Running SysInfo the day my spanking new 4000 arrived. Eric Schwartz animations. Nico Francois and the prolific amount of tools he wrote. Seeing the true power of DOpus. Many things.
I think alot of the good memories and experiences we have stem largely from the fact that computers back then were alot simpler and alot more fun because there was nothing to worry about except for the occasional bootblock virus. If only that were still the case.
*philosophical, wistful mode off but reserved for later use*